Saturn's F Ring: Kinematics and Particle Sizes from Stellar Occultation Studies

The occultation of GSC5249-01240 by Saturn's rings was observed in a spectrally resolved mode using the Faint Object Spectrograph on the Hubble Space Telescope. By combining these data with other occultation data, we have determined the inclination of the F ring to be 0.0065±0.0014 deg. Our inclined F ring orbit model explains an abrupt decrease in flux at the west ansa of the ring that was observed during the November 1995 ring-plane crossing as well as the nondetection of 1995 S5 during one set of observations in November 1995. The F ring's equivalent depth is found to have no significant dependence on wavelength between 0.27 and 0.74 μm, indicating the presence of a population of ring particles larger in size than ∼10 μm. This contrasts with the results from a previous analysis of Voyager images at various phase angles, in which the particles were determined to be predominantly submicron in size. The difference may be due to temporal or longitudinal variability within the ring.     

Moonlet Collisions and the Effects of Tidally Modified Accretion in Saturn's F Ring

We both test and offer an alternative to a meteoroid bombardment model (M. R. Showalter 1998, Science282, 1099-1102) and suggest that anomalous localized brightenings in the F ring observed by Voyager result from disruptive collisions involving poorly consolidated moonlets, or “rubble piles.” This model can also explain the transient events observed during ring plane crossing. We have developed an evolutionary model that considers both the competing effects of accretion and disruption at the location of the F ring. Our numerical model is a Markov process where probabilities of mass transfer between the states of the system form a “transition matrix.” Successive multiplications of this matrix by the state vector generate expectation values of the distribution after each time step as the system approaches quasi-equilibrium. Competing effects of accretion and disruption in the F ring are found to lead to a bimodal distribution of ring particle sizes. In fact, our simulation predicts the presence of a belt of kilometer-sized moonlets in the F ring. These moonlets may continually disrupt one another and re-accrete on short time scales. We also agree with J. N. Cuzzi and J. A. Burns (1988, Icarus74, 284-324), who suggest that the classical F ring itself may be the consequence of a relatively recent collision between two of the largest of these yet unseen objects. Cassini observations can confirm the existence of the moonlet belt by directly observing these objects or the waves they create in the rings.     

The Composition of Saturn's Rings

A composite spectrum between 0.30 and 4.05 μm of Saturn's rings is analyzed using the Shkuratov scattering theory (Shkuratov et al. 1999, Icarus137, 235-246). Several types of surface and composition are discussed. We demonstrate that both the strong reddening over the interval 0.3-0.7 μm and the water ice absorption features are well reproduced by an intimate (“salt-and-pepper”) mixture of four coarse particles of two different materials: 93% are grains (typical sizes of 10, 200, and 2000 μm) of water ice containing a few percent of refractory organic solid (tholin) impurities within their bulk, and 7% are coarse grains of a dark material (amorphous carbon). The cosmogenic implications of the inferred composition are discussed.     

HST observations of spokes in Saturn's B ring

As part of a long-term study of Saturn's rings, we have used the Hubble Space Telescope's (HST) Wide Field and Planetary Camera (WFPC2) to obtain several hundred high resolution images from 1996 to 2004, spanning the full range of ring tilt and solar phase angles accessible from the Earth. Using these multiwavelength observations and HST archival data, we have measured the photometric properties of spokes in the B ring, visible in a substantial number of images. We determined the spoke particle size distribution by fitting the wavelength-dependent extinction efficiency of a prominent, isolated spoke, using a Mie scattering model. Following Doyle and Grün (1990, Icarus 85, 168-190), we assumed that the spoke particles were sub-micron size spheres of pure water ice, with a Hansen-Hovenier size distribution (Hansen and Hovenier, 1974, J. Atmos. Sci. 31, 1137-1160). The WFPC2 wavelength coverage is broader than that of the Voyager data, resulting in tighter constraints on the nature of spoke particles. The effective particle size was reff=0.57±0.05 μm, and the size distribution was quite narrow with a variance of b=0.09±0.03, very similar to the results of Doyle and Grün (1990, Icarus 85, 168-190), and consistent with predictions of plasma cloud models for spoke production from meteoritic impacts (Goertz and Morfill, 1983, Icarus 53, 219-229; Goertz, 1984, Adv. Space Res. 4, 137-141). In all, we identified 36 spokes or spoke complexes, predominantly on the morning (east) ansa. The photometric contrast of the spokes is strongly dependent on effective ring opening angle, Beff. Spokes were clearly visible on the north face of the rings in 1994, just prior to the most recent ring plane crossing (RPX) epoch, and on the south face shortly after RPX. However, spokes were both less abundant and fainter as the rings opened up, and no spokes were detected after 18 October 1998 (Beff=−15.43°), when a single faint spoke was seen on the morning ansa. The high resolution and photometric quality of the WFPC2 images enabled us to set a detection limit of ?1% in fractional brightness contrast for spokes for the post-1998 observations. We compare the observed trend of spoke contrast with Beff to radiative transfer calculations based on three models of the distribution of spoke material. In the first, the spoke “haze” is uniformly mixed with macroscopic B ring particles. No variation in spoke contrast is predicted for single-scattering, in this case, and only a modest decrease in contrast with Beff is predicted when multiple scattering is taken into account. In the second model, the spoke dust occupies an extended layer that is thicker than the B ring, which gives virtually identical results to a third case, when the haze layer lies exclusively above the ring. Multiple-scattering Monte Carlo calculations for these two extended haze models match the trend of spoke contrast exceptionally well. We compute the predicted spoke contrast for a wide variety of viewing geometries, including forward- and backscattering. Based on these results, spokes should be easily detectable during the Cassini mission when the rings are viewed at relatively small (|B|?10°) ring opening angles.     

HST observations of azimuthal asymmetry in Saturn's rings

From 378 Hubble Space Telescope WFPC2 images obtained between 1996-2004, we have measured the detailed nature of azimuthal brightness variations in Saturn's rings. The extensive geometric coverage, high spatial resolution (), and photometric precision of the UBVRI images have enabled us to determine the dependence of the asymmetry amplitude and longitude of minimum brightness on orbital radius, ring elevation, wavelength, solar phase angle, and solar longitude. We explore a suite of dynamical models of self-gravity wakes for two particle size distributions: a single size and a power law distribution spanning a decade in particle radius. From these N-body simulations, we calculate the resultant wake-driven brightness asymmetry for any given illumination and viewing geometry. The models reproduce many of the observed properties of the asymmetry, including the shape and location of the brightness minimum and the trends with ring elevation and solar longitude. They also account for the “tilt effect” in the A and B rings: the change in mean ring brightness with effective ring opening angle, |Beff|. The predicted asymmetry depends sensitively on dynamical ring particle properties such as the coefficient of restitution and internal mass density, and relatively weakly on photometric parameters such as albedo and scattering phase function. The asymmetry is strongest in the A ring, reaching a maximum amplitude A∼25% near a=128,000 km. Here, the observations are well-matched by an internal particle density near 450 kg m⁻³ and a narrow particle size distribution. The B ring shows significant asymmetry (∼5%) in regions of relatively low optical depth (τ∼0.7). In the middle and outer B ring, where τ?1, the asymmetry is much weaker (∼1%), and in the C ring, A<0.5%. The asymmetry diminishes near opposition and at shorter wavelengths, where the albedo of the ring particles is lower and multiple-scattering effects are diminished. The asymmetry amplitude varies strongly with ring elevation angle, reaching a peak near |Beff|=10° in the A ring and at |Beff|=15-20° in the B ring. These trends provide an estimate of the thickness of the self-gravity wakes responsible for the asymmetry. Local radial variations in the amplitude of the asymmetry within both the A and B rings are probably caused by regional differences in the particle size distribution.     

More Microwave Observations of Saturn: Modeling the Ring with a Monte Carlo Radiative Transfer Code

We present a second epoch of Very Large Array Saturn observations taken in February 1997 spanning wavelengths 1.3-21 cm. These observations complement earlier observations at Saturn's autumnal equinox in November 1995. In this epoch, however, we generally have better signal-to-noise ratios and the ring inclination of the present observations was −5.0°, whereas the previous observations were made with ring inclination +2.7°.Our observations confirm the latitudinal structure on the saturnian disk as seen at 2.0, 3.6, and 6.1 cm. We also see some latitudinal structure at 1.3 cm for the first time. The details of this structure have changed dramatically from those reported by I. de Pater and J. R. Dickel (1991, Icarus94, 474-492) for the 1980s and are consistent with those seen in F. van der Tak et al. (1999, Icarus142, 125-147). The most prominent features are a pair of brightness enhancements just inside the edges of the Equatorial Zone.The rings do not show the east-west asymmetry seen in our previous epoch, perhaps indicative of a viewing angle effect on the scattering properties of the rings. The radial trend in brightness in the ansae is generally consistent with that expected from optical depth variations and increasing distance from the source of scattered light. In particular the increased optical depth towards the center of the C ring is evident. Azimuthal variation in brightness in the C ring shows the forward scattering expected of Mie scattering. By contrast, the A and B rings show little or no azimuthal variation.We present Monte Carlo simulations of the ring brightness under the assumptions of isotropic and Mie scattering. These are the first synthetic maps of Saturn which can be directly compared to the images we obtained. Neither model fits all the data well. However, a hybrid model combining isotropic and Mie scattering does fit well. We interpret the consistency with isotropic scattering in the outer rings as an indication that near-field effects may be important. This in turn implies geometrically thin rings, as predicted by dynamical simulations of these rings.     

Disentangling Saturn's F Ring. I. Clump orbits and lifetimes

A comprehensive analysis of the Voyager images reveals the kinematics and lifetimes of clumps in the F Ring. At any given time, the ring has 2-3 major clumps, each several times brighter than the typical ring, plus numerous smaller features. A total of 34 individual clumps have been tracked over periods of 1-7 weeks. The clumps orbited at measurably different rates, implying a 100-km range of semimajor axes centered on 140,220 km. Most are centered around the nominal mean motion of the ring's core, but a few outliers may be associated with a different strand, or with no strand at all. Most clumps change very little over the ∼30 days that they can be detected; however, no clump persisted for the nine-month interval between the two Voyager encounters. The brightest Voyager 2 clump is unusual in that it travels at a rapid mean motion and seems to be associated with the formation of several other clumps.     

Saturn's rings, the Yarkovsky effects, and the Ring of Fire

Saturn's icy ring particles, with their low thermal conductivity, are almost ideal for the operation of the Yarkovsky effects (photon thrust due to temperature gradients across the ring particles). An extremely simple case of the Yarkovsky effects is examined here, in which orbital evolution is computed as though each particle travels around Saturn alone in a circular orbit, so that there are no collisions, shadowing, or irradiance from other particles; nor are resonances, tumbling, or micrometeoroid erosion considered. The orbital evolution for random spin orientations appears to be a competition between two effects: the seasonal Yarkovsky effect, which makes orbits contract, and the Yarkovsky-Schach effect, which makes orbits expand. There are values of the far infrared and visible particle albedos for which (working radially out from the planet) the along-track particle acceleration S is negative, then positive, and then negative again; the region for which S>0 is interpreted as a region where stable rings are possible. Typical timescales for centimeter-sized particles to travel half a Saturn radius are ¹⁰⁷-¹⁰⁸ yr. Collisions, shadowing, and resonances may lengthen the timescales, perhaps considerably. It is speculated here that the C ring may be depleted of particles because of the seasonal Yarkovsky effect, and small particles that are present in the C ring ultimately fall on Saturn, possibly creating a “Ring of Fire” as they enter the planet's atmosphere.     

A close look at Saturn's rings with Cassini VIMS

Soon after the Cassini-Huygens spacecraft entered orbit about Saturn on 1 July 2004, its Visual and Infrared Mapping Spectrometer obtained two continuous spectral scans across the rings, covering the wavelength range 0.35-5.1 μm, at a spatial resolution of 15-25 km. The first scan covers the outer C and inner B rings, while the second covers the Cassini Division and the entire A ring. Comparisons of the VIMS radial reflectance profile at 1.08 μm with similar profiles at a wavelength of 0.45 μm assembled from Voyager images show very little change in ring structure over the intervening 24 years, with the exception of a few features already known to be noncircular. A model for single-scattering by a classical, many-particle-thick slab of material with normal optical depths derived from the Voyager photopolarimeter stellar occultation is found to provide an excellent fit to the observed VIMS reflectance profiles for the C ring and Cassini Division, and an acceptable fit for the inner B ring. The A ring deviates significantly from such a model, consistent with previous suggestions that this region may be closer to a monolayer. An additional complication here is the azimuthally-variable average optical depth associated with “self-gravity wakes” in this region and the fact that much of the A ring may be a mixture of almost opaque wakes and relatively transparent interwake zones. Consistently with previous studies, we find that the near-infrared spectra of all main ring regions are dominated by water ice, with a typical regolith grain radius of 5-20 μm, while the steep decrease in visual reflectance shortward of 0.6 μm is suggestive of an organic contaminant, perhaps tholin-like. Although no materials other than H₂O ice have been identified with any certainty in the VIMS spectra of the rings, significant radial variations are seen in the strength of the water-ice absorption bands. Across the boundary between the C and B rings, over a radial range of ∼7000 km, the near-IR band depths strengthen considerably. A very similar pattern is seen across the outer half of the Cassini Division and into the inner A ring, accompanied by a steepening of the red slope in the visible spectrum shortward of 0.55 μm. We attribute these trends—as well as smaller-scale variations associated with strong density waves in the A ring—to differing grain sizes in the tholin-contaminated icy regolith that covers the surfaces of the decimeter-to-meter sized ring particles. On the largest scale, the spectral variations seen by VIMS suggest that the rings may be divided into two larger ‘ring complexes,’ with similar internal variations in structure, optical depth, particle size, regolith texture and composition. The inner complex comprises the C and B rings, while the outer comprises the Cassini Division and A ring.     

Self-gravity wakes and radial structure of Saturn's B ring

We analyze stellar occultations by Saturn's rings observed with the Cassini Ultraviolet Imaging Spectrograph and find large variations in the apparent normal optical depth of the B ring with viewing angle. The line-of-sight optical depth is roughly independent of the viewing angle out of the ring plane so that optical depth is independent of the path length of the line-of-sight. This suggests the ring is composed of virtually opaque clumps separated by nearly transparent gaps, with the relative abundance of clumps and gaps controlling the observed optical depth. The observations can be explained with a model of self-gravity wakes like those observed in the A ring. These trailing spiral density enhancements are due to the competing processes of self-gravitational accretion of ring particles and Kepler shear. The B ring wakes are flatter and more closely packed than their neighbors in the A ring, with height-to-width ratios <0.1 for most of the ring. The self-gravity wakes are seen in all regions of the B ring that are not opaque. The observed variation in total B ring optical depth is explained by the amount of relatively empty space between the self-gravity wakes. Wakes are more tightly packed in regions where the apparent normal optical depth is high, and the wakes are more widely spaced in lower optical depth regions. The normal optical depth of the gaps between the wakes is typically less than 0.5 and shows no correlation with position or overall optical depth in the ring. The wake height-to-width ratio varies with the overall optical depth, with flatter, more tightly packed wakes as the overall optical depth increases. The highly flattened profile of the wakes suggests that the self-gravity wakes in Saturn's B ring correspond to a monolayer of the largest particles in the ring. The wakes are canted to the orbital direction in the trailing sense, with a trend of decreasing cant angle with increasing orbital radius in the B ring. We present self-gravity wake properties across the B ring that can be used in radiative transfer modeling of the ring. A high radial resolution (∼10 m) scan of one part of the B ring during a grazing occultation shows a dominant wavelength of 160 m due to structures that have zero cant angle. These structures are seen at the same radial wavelength on both ingress and egress, but the individual peaks and troughs in optical depth do not match between ingress and egress. The structures are therefore not continuous ringlets and may be a manifestation of viscous overstability.     

Structure of self-gravity wakes in Saturn's A ring as measured by Cassini CIRS

The CIRS infrared spectrometer onboard the Cassini spacecraft has scanned Saturn's A ring azimuthally from several viewing angles since its orbit insertion in 2004. A quadrupolar asymmetry has been detected in this ring at spacecraft elevations ranging between 16° to 37°. Its fractional amplitude decreases from 22% to 8% from 20° to 37° elevations. The patterns observed in two almost complete azimuthal scans at elevations 20° and 36° strongly favor the self-gravity wakes as the origin of the asymmetry. The elliptical, infinite cylinder model of Hedman et al. [Hedman, M.M., Nicholson, P.D., Salo, H., Wallis, B.D., Buratti, B.J., Baines, K.H., Brown, R.H., Clark, R.N., 2007. Astron. J. 133, 2624-2629] can reproduce the CIRS observations well. Such wakes are found to have an average height-to-spacing ratio H/λ=0.1607±0.0002, a width-over-spacing W/λ=0.3833±0.0008. Gaps between wakes, which are filled with particles, have an optical depth τG=0.1231±0.0005. The wakes mean pitch angle ΦW is 70.70°±0.07°, relative to the radial direction. The comparison of ground-based visible data with CIRS observations constrains the A ring to be a monolayer. For a surface mass density of 40 g cm⁻² [Tiscarino, M.S., Burns, J.A., Nicholson, P.D., Hedman, M.M., Porco, C.C., 2007. Icarus 189, 14-34], the expected spacing of wakes is λ≈60 m. Their height and width would then be H≈10 m and W≈24 m, values that match the maximum size of particles in this ring as determined from ground-based stellar occultations [French, R.G., Nicholson, P.D., 2000. Icarus 145, 502-523].     

Study of the vertical structure of Saturn's atmosphere using HST/WFPC2 images

We have studied the vertical structure of hazes at six different latitudes (−60°, −50°, −30°, −10°, +30°, and +50°) on Saturn's atmosphere. For that purpose we have compared the results of our forward radiative transfer model to limb-to-limb reflectivity scans at four different wavelengths (230, 275, 673.2, and 893 nm). The images were obtained with the Hubble Space Telescope Wide Field Planetary Camera 2 in September 1997, during fall on Saturn's northern hemisphere. The spatial distribution of particles appears to be very variable with latitude both in the stratosphere and troposphere. For the latitude range +50° to −50°, an atmospheric structure consisting of a stratospheric haze and a tropospheric haze interspersed by clear gas regions has been found adequate to explain the center to limb reflectivities at the different wavelengths. This atmospheric structure has been previously used by Ortiz et al. (1996, Icarus 119, 53-66) and Stam et al. (2001, Icarus 152, 407-422). In this work the top of the tropospheric haze is found to be higher at the southern latitudes than at northern latitudes. This hemispherical asymmetry seems to be related to seasonal effects. Different latitudes experience different amount of solar insolation that can affect the atmospheric structure as the season varies with time. The haze optical thickness is largest (about 30 at 673.2 nm) at latitudes ±50 and −10 degrees, and smallest (about 18) at ±30 degrees. The stratospheric haze is found to be optically thin at all studied latitudes from −50 to +50 degrees being maximum at −10° (τ=0.033). At −60° latitude, where the UV images show a strong darkening compared to other regions on the planet, the cloud structure is remarkably different when compared to the other latitudes. Here, aerosol and gas are found to be uniformly mixed down to the 400 mbar level.     

Apse Alignment of the Uranian Rings

An explanation of the dynamical mechanism for apse alignment of the eccentric uranian rings is necessary before observations can be used to determine properties such as ring masses, particle sizes, and elasticities. The leading model (P. Goldreich and S. Tremaine 1979, Astron J.84, 1638-1641) relies on the ring self-gravity to accomplish this task, yet it yields equilibrium masses which are not in accord with Voyager radio measurements. We explore possible solutions such that the self-gravity and the collisional terms are both involved in the process of apse alignment. We consider limits that correspond to a hot and a cold ring, and we show that pressure terms may play a significant role in the equilibrium conditions for the narrow uranian rings. In the cold ring case, where the scale height of the ring near periapse is comparable to the ring particle size, we introduce a new pressure correction pertaining to a region of the ring where the particles are locked in their relative positions and jammed against their neighbors and the velocity dispersion is so low that the collisions are nearly elastic. In this case, we find a solution such that the ring self-gravity maintains apse alignment against both differential precession (m=1 mode) and the fluid pressure. We apply this model to the uranian α ring and show that, compared to the previous self-gravity model, the mass estimate for this ring increases by an order of magnitude. In the case of a hot ring, where the scale height can reach a value as much as 50 times the particle size, we find velocity dispersion profiles that result in pressure forces which act in such a way as to alter the ring equilibrium conditions, again leading to a ring mass increase of an order of magnitude. We find that such a velocity dispersion profile would require a different mechanism than is currently envisioned for establishing a heating/cooling balance in a finite-sized, inelastic particle ring. Finally, we introduce an important correction to the model of E. I. Chiang and P. Goldreich (2000, Astrophys. J.540, 1084-1090.). These authors relied on collisional forces in the last ∼100 m of an ∼10 km wide ring to increase ring equilibrium masses by up to a factor of ∼100. However, their treatment of ring edges as one-sided surface density drops leads to a strong dependence of the ring mass on the adjustable parameter λ (the length scale over which the ring's optical depth drops from order unity to zero at the edge). A treatment of the ring edges that takes into account their ridgelike structure retains the increase of ring mass of the order of ∼100 for a 10 km wide ring, while exhibiting weak dependence on λ. We conclude that a modified Chiang-Goldreich model can likely account for the masses of narrow, eccentric planetary rings; however, the role of shepherd satellites both in forming ring edges and in altering the streamline precession conditions near them needs to be explored further. It is also unclear whether a fully self-consistent ring model allows for the possibility of rings with negative eccentricity gradients.     

A procedure to analyze nonlinear density waves in Saturn's rings using several occultation profiles

Cassini radio science experiments have provided multiple occultation optical depth profiles of Saturn's rings that can be used in combination to analyze density waves. This paper establishes an accurate procedure of inversion of the wave profiles to reconstruct the wave kinematic parameters as a function of semi-major axis, in the nonlinear regime. This procedure is established using simulated data in the presence of realistic noise perturbations, to control the reconstruction error. It is then applied to the Mimas 5:3 density wave. There are two important concepts at the basis of this procedure. The first one is that it uses the nonlinear representation of density waves, and the second one is that it relies on a combination of optical depth profiles instead of just one profile. A related method to analyze density waves was devised by Longaretti and Borderies [Longaretti, P.-Y., Borderies, N., 1986. Icarus 67, 211-223] to study the nonlinear density wave associated with the Mimas 5:3 resonance, but the single photopolarimetric profile provided limited constraints. Other studies of density waves analyzing Cassini data [Colwell, J.E., Esposito, L.W., 2007. Bull. Am. Astron. Soc. 39, 461; Tiscareno, M.S., Burns, J.A., Nicholson, P.D., Hedman, M.M., Porco, C.C., 2007. Icarus 189, 14-34] are based on the linear theory and find inconsistent results from profile to profile. Multiple cuts of the rings are helpful in a fundamental way to ensure the accuracy of the procedure by forcing consistency among the various optical depth profiles. By way of illustration we have applied our procedure to the Mimas 5:3 density wave. We were able to recover precisely the kinematic parameters from the radio experiment occultation data in most of the propagation region; a preliminary analysis of the pressure-corrected dispersion allowed us to determine new but still uncertain values for the opacity (K?0.02 cm²/g) and velocity dispersion of (c₀?0.6 cm/s) in the wave region. Our procedure constitutes the first step in our planned analysis of the density waves of Saturn's rings. It is very accurate and efficient in the far-wave region. However, improvements are required within the first wavelength. The ways in which this method can be used to establish diagnostics of ring physics are outlined.     

Spinning particles in Saturn's C ring from mid-infrared observations: Pre-Cassini mission results

Saturn's C ring thermal emission has been observed in mid-infrared wavelengths, at three different epochs and solar phase angles, using ground based instruments (CFHT in 1999 and VLT/ESO in 2005) and the Infrared Radiometer Instrument Spectrometer (IRIS) onboard the Voyager 1 spacecraft in 1980. Azimuthal variations of temperature in the C ring's inner region, observed at several phase angles, have been analyzed using our new standard thermal model [Ferrari, C., Leyrat, C., 2006. Astron. Astrophys. 447, 745-760]. This model provides predicted ring temperatures for a monolayer ring composed of spinning icy spherical particles. We confirm the very low thermal inertia (on the order of 10 ) found previously by Ferrari et al. [Ferrari, C., Galdemard, P., Lagage, P.O., Pantin E., Quoirin, C., 2005. Astron. Astrophys. 441, 379-389] that reveals the very porous regolith at the surface of ring particles. We are able to explain both azimuthal variations of temperature and the strong asymmetry of the emission function between low and high phase angles. We show that large particles spinning almost synchronously might be present in the C ring to explain differences of temperature observed between low and high phase angle. Their cross section might represent about 45% of the total cross section. However, their numerical fraction is estimated to only ∼0.1% of all particles. Thermal behavior of other particles can be modeled as isothermal behavior. This work provides an indirect estimation of the particle's rotation rate in Saturn's rings from observations.     

Gravitational accretion of particles in Saturn's rings

Gravitational accretion in the rings of Saturn is studied with local N-body simulations, taking into account the dissipative impacts and gravitational forces between particles. Common estimates of accretion assume that gravitational sticking takes place beyond a certain distance (Roche distance) where the self-gravity between a pair of ring particles exceeds the disrupting tidal force of the central object, the exact value of this distance depending on the ring particles' internal density. However, the actual physical situation in the rings is more complicated, the growth and stability of the particle groups being affected also by the elasticity and friction in particle impacts, both directly via sticking probabilities and indirectly via velocity dispersion, as well as by the shape, rotational state and the internal packing density of the forming particle groups. These factors are most conveniently taken into account via N-body simulations. In our standard simulation case of identical 1 m particles with internal density of solid ice, ρ=900 kg m⁻³, following the Bridges et al., 1984 elasticity law, we find accretion beyond a=137,000-146,000 km, the smaller value referring to a distance where transient aggregates are first obtained, and the larger value to the distance where stable aggregates eventually form in every experiment lasting 50 orbital periods. Practically the same result is obtained for a constant coefficient of restitution εn=0.5. In terms of rp parameter, the sum of particle radii normalized by their mutual Hill radius, the above limit for perfect accretion corresponds to rp<0.84. Increased dissipation (εn=0.1), or inclusion of friction (tangential force 10% of normal force) shifts the accretion region inward by about 5000 km. Accretion is also more efficient in the case of size distribution: with a q=3 power law extending over a mass range of 1000, accretion shifts inward by almost 10,000 km. The aggregates forming in simulations via gradual accumulation of particles are synchronously rotating.     

Microwave observations of Saturn's rings: anisotropy in directly transmitted and scattered saturnian thermal emission

We present a new Very Large Array (VLA) image of Saturn, made from data taken in October 1998 at a wavelength of λ3.6 cm. The moderate ring opening angle (B≈15°) allows us to explore direct transmission of microwave photons through the A and C rings. We find a strong asymmetry of photons transmitted through the A ring, but not in the C ring, a new diagnostic of wake structure in the ring particles. We also find a weak asymmetry between east and west for the far side of the ansae. To facilitate quantitative comparison between dynamic models of the A ring and radio observations, we extend our Monte Carlo radiative transfer code (described in Dunn et al., 2002, Icarus 160, 132-160) to include idealized wakes. We show the idealized model can reproduce the properties of dynamic simulations in directly transmitted light. We examine the model behavior in directly transmitted and scattered light over a range of physical and geometric wake parameters. Finally, we present a wake model with a plausible set of physical parameters that quantitatively reproduces the observed intensity and asymmetry of the A ring both across the planet and in the ansae.     

Saturn's vertical and latitudinal cloud structure 1991-2004 from HST imaging in 30 filters

We analyzed 134 images of Saturn taken by the Hubble Space Telescope between 1991 and 2004. The images cover wavelengths between 231 and 2370 nm in 30 filters. We combined some 10 million calibrated reflectivity measurements into 18,000 center-to-limb curves. We used the method of principal component analysis to find the main latitudinal and temporal variations in Saturn's atmosphere and their spectral characteristics. The first principal variation is a strong latitudinal variation of the aerosol optical depth in the upper troposphere. This structure shifts with Saturn's seasons, but the structure on small scales of latitude stays constant. The second principal variation is a variable optical depth of stratospheric aerosols. The optical depth is large at the poles and small at mid- and low latitudes with a steep gradient in-between. This structure remains essentially constant in time. The third principal variation is a variation in the tropospheric aerosol size, which has only shallow gradients with latitude, but large seasonal variations. Thus, aerosol sizes and their phase functions inferred at a particular season are not representative of Saturn's atmosphere at other seasons. Aerosols are largest in the summer and smallest in the winter. The fourth principal variation is a feature of the tropospheric aerosols with irregular latitudinal structure and fast variability, on the time scale of months. Spherical aerosols do not display the spectral characteristic of that feature. We suspect that variations in the shape of aerosols may play a role. We found a spectral feature of the imaginary index of aerosols, which darkens them near 400 nm wavelength. While we can describe Saturn's variations quite accurately, our presented model of Saturn's average atmosphere is still uncertain due to possible systematic offsets in methane absorption data and limitations of the knowledge about the shape of aerosols. In order to compare our results with those from comparable investigations, which used less than 30 filters, we fit models to spectral subsets of our data. We found very different best-fitting models, depending on the subset of filters, indicating a high sensitivity of results on the spectral sampling.     

The composition of Saturn's E ring

We present the first in situ direct measurement of the composition of particles in Saturn's rings. The Cassini cosmic dust analyser (CDA) measured the mass spectra of nearly 300 impacting dust particles during the 2004 October E ring crossing. An initial interpretation of the data shows that the particles are predominantly water ice, with minor contributions from possible combinations of silicates, carbon dioxide, ammonia, molecular nitrogen, hydrocarbons and perhaps carbon monoxide. This places constraints on both the composition of Enceladus, the main source of the E ring, as well as the grain formation mechanisms.     

On the damping of the bending waves in Saturn’s ring

We study numerically the motion of a single particle in the bending wave of finite thickness in Saturn’s ring. We include the forcing due to the planet, a moon, the coriolis force and the self gravity of the ring. In particular, we compute the variation of the velocity arising due to the variation of the amplitude and the phase of the epicyclic motion across the local vertical height of the ring. We suggest that the dissipation of energy due to the collision of ring particles in this shear layer damps out the bending wave of Saturn’s ring at the 5:3 vertical resonance of Mimas within a distance of 150 km from the site of its launching as is observed in Voyager data.